Problem: Solve for $n$. $\left(2^4\right)^{2}=2^n$ $n=$
The general rule for powers of powers is $\left(x^m\right)^{n}=x^{m\cdot n}$. Let's expand the powers for $ \left({2^4}\right)^{{2}}=2^n}$. $\begin{aligned} \left({2^4}\right)^{2}&=\underbrace{{2^4\cdot 2^4}}_{\text{2 times}} \\\\\\ &=\underbrace{ \underbrace{{2\cdot 2\cdot 2 \cdot 2}}_\text{4 times} \cdot \underbrace{{2\cdot 2\cdot 2 \cdot 2}}_\text{4 times}} _{\text{2 times}} \\\\ &=\underbrace{2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot \cdot 2 \cdot 2}_{n\text{ times}}} \\\\ \end{aligned}$ $n = 8$